This invention relates generally to systems which detect simultaneity of events, and more particularly, to a detection system which performs a Maximum Likelihood Estimation (MLE) of a pulse arrival time, the system being particularly adaptable to high energy physics and positron emission tomography (PET).
The two most widely used systems for timing events, such as in positron emission tomography, are leading-edge timing and constant-fraction timing. In PET scanning systems, it is desired to identify the location of a positron source, particularly within the body of a living being, during medical diagnosis. This is achieved by detecting a pair of oppositely traveling gamma rays which are issued when a positron is annihilated by collision with an electron. The gamma rays are issued substantially in directions 180.degree. from one another, and by detecting the locations of the two gamma rays, the position of the annihilation can be determined to lie along a line between the location of detected gamma rays. Such detection of the gamma rays is achieved by using a plurality of scintillation crystals, which may be formed of sodium iodide crystal, bismuth germanate (BGO), barium fluoride (BaF.sub.2), etc. When the gamma rays interact with the scintillation crystals, a pulse of light is generated which is detected by one or more photomultiplier tubes (PMTs), which, subject to certain statistical processs, convert the light input into an electrical signal.
The accuracy with which one can determine the time difference between the detection of the two gamma rays determines the probability that the two gamma rays originated from a single positron decay, and not two nearly coincidental, but physically unrelated decays. Additionally, as the accuracy of the timing improves, illustratively to the order of a few hundred picoseconds, the relative distance of the positron decay from the two detectors can be estimated because the transit time of the two gamma rays depends upon the distances traveled to the respective detectors. When the output pulses from the two detectors arrive within a predetermined time interval, the pulses are deemed to be coincidental to a single positron decay.
In such systems, there is present a measure of timing uncertainty which results from a variety of factors. One such factor is that the light output from the scintillator crystal has a finite mean rise time and decay time. For any given light pulse there are departures from the mean pulse shape due to the statistical nature of the light emission process. These random variations in shape introduce random variations in the measured time of occurrence of the pulse which depend in part on the method used to measure the time of occurrence. In similar fashion, the photosensor has a finite mean rise time and fall time associated with each photoelectron. Furthermore, there is a transit time variation in PMTs which, in combination with other random effects, result in variations about a mean for the pulse rise time. This time uncertainty, which has been termed "jitter," can be further increased by noise on the detector signal, which can be generated by the detector or within its associated electronics. A further cause of timing uncertainty results from the fact that a wide range of pulse amplitudes are obtained from the scintillator crystal. Thus, input signals having the same rise time, but different amplitudes will cross a detector threshold value at different times after the time of origination of the event. The result is that the output pulse of the detector is caused to "walk" along the time axis. The lower the amplitude of the input signal relative to the threshold, the more pronounced this type of error becomes.
Leading-edge triggering is performed by sensing the pulse with a discriminator circuit which has a very low threshold. This type of a system generates a fast timing spike when the input pulse voltage exceeds the threshold. Thus, a principal objective of this known system is to detect the first few photons given off by the scintillator. This is the simplest type of system for deriving a timing signal, but is quite subject to the aforementioned time walk error especially in cases when the threshold is set much above the first electron level. The time walk error is exacerbated by the charge sensitivity of leading-edge discriminators. In essence, once an input signal crosses the discriminator threshold level, a further amount of charge is required to achieve triggering of the discriminating element. The amount of error generated by this additional energy requirement increases with increases in the rise rate of the input signals. Additionally, such charge sensitivity increases the effective threshold level of the discriminator, resulting in errors which are greater for input signals having steeper leading edge slopes.
Constant-fraction timing aims to generate a timing pulse when the input pulse exceeds a predetermined optimum triggering fraction of the input pulse height. This type of timing arrangement produces less time-walk than leading-edge timing. In constant-fraction timing, the input signal is delayed and a fraction of the undelayed input is subtracted, usually to produce a bipolar pulse. The zero-crossing is detected, such detection causing issuance of an output logic pulse. Timing walk resulting from variations in amplitude and rise time of the input signal are minimized by proper selection of the shaping delay. However, neither leading-edge triggering nor constant-fraction timing overcome completely the problems resulting from statistical variations in pulse shape. Additionally, neither system utilizes all of the information available in an optimal manner. Faster scintillations will give improved timing, but to date these materials have lower stopping power or possess considerable chemical properties. Even with faster scintillators, improved timing will be obtained if all the pulse information is optimally used.
It is, therefore, an object of this invention to provide a timing system having high accuracy for detecting the time of nuclear events.
It is another object of this invention to provide a system which provides high accuracy for detecting simultaneously emitted gamma rays resulting from positron decay.
It is also an object of this invention to provide a high accuracy timing system which can be implemented in PET scanning systems.
It is a further object of this invention to provide a timing system for PET which can achieve timing with sufficient accuracy to provide positron source location based on time-of-flight information.
It is additionally an object of this invention to provide a timing system which provides improvement over leading-edge triggering systems, including first electron timing systems.
It is yet a further object of this invention to provide a timing system which provides improvement over constant-fraction timing systems.
It is also another object of this invention to provide a timing system which provides improvement over conventional amplitude-and-rise-time-compensated timing.
It is yet an additional object of this invention to provide a timing system which provides improvement over conventional true-constant-fraction timing.
It is still another object of this invention to provide a timing system which can be used in gamma-gamma correlation and detection systems which utilize scintillation crystals.
It is a yet further object of this invention to provide timing system which can be implemented using position estimating technology.
It is also a further object of this invention to provide a timing system wherein timing estimation is achieved using a correlation process.
It is additionally another object of this invention to provide a timing system which provides improvement over known arrangements with respect to input signals having variations in amplitudes.
A still further object of this invention is to provide a timing system which provides improvement over known arrangements in its ability to eliminate timing uncertainty resulting from time walking.
An additional object of this invention is to provide a system wherein spatial uncertainty of the location of a positron event is reduced.
Yet another object of this invention is to provide a system for inclusion in a PET scanning systems wherein the signal-to-noise ratio of the image is improved.
Another object of this invention is to provide a timing system for PET which can be incorporated into a multi-channel system.
A yet further object of this invention is to improve the performance of PET imaging instruments with currently available phototubes and scintillators.
It is also an additional object of this invention to provide a system which improves the operation of PET instruments so as to establish a new set of boundary conditions for instrument optimization.